Question: Write the equation of the line in fully simplified slope-intercept form. Graph: a blue decreasing line on a coordinate grid, passing through the points $(-2, 8)$, $(-1, 2)$, $(0, -4)$, and $(1, -10)$, extending upward to the left and downward to the right.

1. **State the problem:** Find the equation of the line passing through the points $(-2, 8)$, $(-1, 2)$, $(0, -4)$, and $(1, -10)$ in slope-intercept form $y = mx + b$. 2. **Formula:** The slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** Use any two points, for example $(-2, 8)$ and $(-1, 2)$. $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 8}{-1 - (-2)} = \frac{-6}{-1 + 2} = \frac{-6}{1} = -6$$ 4. **Find the y-intercept $b$:** Use the slope and one point, for example $(0, -4)$. Since $x=0$, $y = b$, so $b = -4$. 5. **Write the equation:** Substitute $m = -6$ and $b = -4$ into the slope-intercept form. $$y = -6x - 4$$ 6. **Verify with another point:** Check with $(1, -10)$. $$y = -6(1) - 4 = -6 - 4 = -10$$ which matches the point. **Final answer:** $$\boxed{y = -6x - 4}$$